Physics difficult thinking question?

Question

It's about acceleration.

There are two balls. One is heavier than the other. They are of the same material, surface area, everything's the same exp. for the weight.

If i throw the two balls down from mid air( there is air resisitance), the heavire ball will reach the gorund faster. Why?

I need a answer that is written in terms of F=ma. i need to mention the resultant force.

I don't understand why the heavier one will drop faster because i thought ACCELERATION OF FALLING IS THE SAME!.

Answer 1

The acceleration under the force of gravity is the same for both balls, regardless of their mass, 32 feet per second per second down. But there's another force acting on the balls, wind resistance.

If the balls are the same size, then the same surface area is pointing down (that is, in the direction the balls are moving.) But the wind resistance has a greater effect on the lighter ball, since its mass is less.

Let's say the heavier ball is twice the mass of the lighter ball. In scientific terms, there are two separate forces acting. Gravitiational force is directly proportional to mass, F=ma - acceleration is held constant, the heavier ball has twice the mass, and gravity exerts twice the force..

But for the wind resistance, pressure is constant for both balls. Force times area equals pressure, and we have already established that the area of the balls is the same, so it follows that force is constant for both balls. F=ma - this time the force is held constant, the heavier ball has twice the mass, so it gets only half the acceleration (in this case, deceleration) from wind resistance.

So it hits the ground first.

Answer 2

The balls have the same shape and size but different mass.

Let m1 = mass of lighter ball

m2 = mass of heavier ball

On each ball, two forces are acting. One is gravity, which is in downward direction. Another is air resistance in upward direction. Air resistance depends on volume, which is the same for both balls. Therefore, air resistance on both balls is the same.

Let Fair = force of air resistance on each ball.

On ball with mass m1, the two forces are

1. weight = m1g downward

2. air resistance = Fair upward

Therefore, net downward force on m1 = m1g - Fair

Acceleration of m1 = a1 = (m1g - Fair)/m1

Or, a1 = g - Fair/m1--------------(1)

Likewise, acceleration of m2

a2 = g - Fair/m2---------------(2)

From (1) and (2)

a2 - a1 = g - Fair/m2 - (g - Fair/m1)

= g - Fair/m2 - g + Fair/m1

= Fair(1/m1 - 1/m2)

= Fair(m2-m1)/(m1m2)

This is positive because m2 > m1

a2 - a1 > 0

Or, a2 > a1

Thus heavier ball will fall faster.

Answer 3

I think the main issue you're having here is confusing ideal physics world with the real world.

If you completely neglect air resistance, which can only be done in ideal physics world, the two objects will fall at the exact same rate (the acceleration due to gravity will be about 9.81 meters per second squared either way).

However, if you include air resistance, the heavier object will fall faster because of F=ma.  If you imagine two identical bowling balls, one 10 lbs and one 20 lbs, both falling at 100 miles per hour... since they're the same size going the same speed, the upward force due to air resistance will be equal, and that force affects acceleration more on the ball with lower mass (due to F=ma).

Answer 4

The acceleration from gravity is the same but you yourself mentioned air resistance. There are therefore two forces acting on the ball and it is the resultant force from these that governs the motion of the ball. Gravity is pulling the ball down but drag is pushing in the opposite direction and slowing the descent of the ball.

Air resistance or drag for small objects moving at relatively slow speed can be expressed as:

D = -b*V

Where b is a constant and depends on density of air and the dimensions of the ball. Since these are the same for both balls, b will be the same for both.

Newton says that:

(resultant force) = mass*acceleration

(gravity) + (drag) = m*a

m*g - b*V = m*a

Since the drag depends on the velocity, the faster the ball falls the larger drag becomes. Eventually drag will equal the force of gravity and the ball will stop accelerating. At this point a = 0. So:

m*g - b*V = 0

V = mg/b

So the velocity of the ball is a constant at this point and depends just on the mass of the ball. Twice the mass and the ball will fall twice as fast.

Answer 5

You have it - or almost.

You see that, although the acceleration is the same for both balls, the force from gravity is NOT the same. Gravity will exert more force on the heavier ball. (Newton noticed that between gravity and inertia, things fell at the same speed. We think that is obvious, but really it is not obvious. It simply IS that way!)

Then the air resistance will create an opposing force. But since the air resistance is only dependent on the area and shape of the ball, at any speed, it will be the same for each ball.

You know that an object accelerates according to the net force, the resultant force, applied to it, and the net force is the vector sum of all of the forces. Since this motion is just in a single line, you can treat the vectors as simple numbers and add them.

When you add the positive force of gravity and the negative force of air resistance, you come up with the net force - the 'resultant' force, and you can see that the same negative force will have a smaller (percentage) effect on the larger ball, so it will fall faster.

The reason you get a different acceleration is that F=ma, but the a, the acceleration,  is the acceleration of gravity MINUS the acceleration caused by the air resistance.